Answer and Explanation:
Solution:
Let x and y are independent, ariables.
The parameters of x and y are (n1, p) and (n2, p), respectively.
It means the sum of the independent binomial variable is itself a binomial random variable.
Consider probability of the event [ x = n1],
Denoted by: p(x=n1)
The function:
P(n1) = p(x = n1)
Over the possible value of x say, n1, n2, n3, …, is called frequency function.
The frequency function must satisfy.
∑I p (ni) = 1,
Where the sum is possible values of x.
Similarly,
Consider probability of the event [ y = n2],
Denoted by: p(y=n2)
The function:
P (n2) = p(y = n2)
Over the possible value of y say, n1, n2, n3, …, is called frequency function.
The frequency function completely describes the probabilistic nature of the random variable.
